Can you cast a spell during the end step if an opponent passes priority first?

Priority determines who may take actions at any given moment. During the end step (a step within the ending phase), the active player receives priority first after the end step begins and any triggered abilities resolve. Players may cast instants and activate abilities whenever they have priority, including during the end step — CR 116.1 and 500.2.

Once a player passes priority, the next player in turn order receives it (CR 117.3d). If your opponent (the active player) passes priority to you during the end step, you now hold priority and may cast any instant-speed spell or activate abilities. The step does not end until all players pass priority in succession with the stack empty (CR 500.2).

It is important to note that sorcery-speed spells cannot be cast during the end step regardless of who passes priority, because you are not in a main phase with an empty stack and you do not have priority as the active player (CR 307.1). Only instants and cards/effects with flash or similar abilities are eligible.

Concrete example: It is your opponent's turn and they pass priority during the end step. You cast Opt (an instant) in response. You now hold priority again after casting it; once you pass and your opponent passes with Opt on the stack, it resolves. Then priority returns to the active player — if no one does anything further and both players pass again, the end step concludes.

So the condition is simple: you must hold priority (which you do after an opponent passes to you), and the spell you cast must be an instant or have flash (CR 116.1, 117.3d, 500.2).